Small samples confidencce intervals on common mean of two normal distributions variances

Let X₁,X₂,…,X_m be distributed normally with mean μ and variance σ² _X; Let Y₁,Y₂,…,Y_n be distributed normally with mean μ and variance σ² _Y; let X₁,X₂,…,X_m,Y₁,Y₂,…,Y_n be jointly independent. There have been several papers written concerning point estimation of μ for this problem, but very little is available in the literature concerning confidence intervals on the common mean μ. In this paper a method is proposed that results in a confidence interval with confidence coefficient essentially equal to a prescribed value 1 - α. The method is evaluated and compnred with other methods through the expected length of the confidence interval.